The problem is it's a line of dead pixels. The only way to resolve it is to have the screen replaced. Some people have tried apps that flash random colors and they claim if you have leave it running long enough it will fix it. My years of experience tell me otherwise.

There are 3 sub-pixels ( Red, Green, Blue ) for each pixel. If the transistor that controls the pixel is not receiving power, it may only be passing light at that point. In your case, they are always green.

If you just don't care if it can get worse you can try to dissasemble the metal frame from the screen, not from the laptop but the screen itself.

First you can, with some care, try to press all around then edges of the screen.

If you are more desperate in some screens (I never did it on a Mac) you can clean the rubber that makes the contact between the glass and the board, but you need to completly dissasemble the screen.

What happens is that most of the times a complete line failing is a bad contact in one point and there is no power going to the line.

Of corse if you brake the screen you can end up with the same effect and this wont solve anything.